In free electron lasers, the radiation is obtained by the modulation of the electron impulse in a vacuum. The Maxwell equations describe the radiation emitted by an electrical charge that undergoes an impulse variation dp due to an external field F, generally in the presence of electrical and magnetic fields. The amplitude of the radiation varies as a function of the of the variation of the impulse dp.
The amplitude of the electron radiation emitted by an electrical charge in non-uniform motion depends on the mass m of the particle, the variation in energy being distributed among a variation in mass, a variation in velocity and a radiation.
The intensity of the radiation is all the greater as the acceleration or, more precisely, the variation in the impulse of the particle is greater (this covers variations in both mass and position). In particle accelerators with a circular geometry, in which the particles are forced, by magnetic fields, to follow circular orbits and, consequently, undergo a constant variation of their the radiation emitted by particles of low mass (such as electrons or positrons) is particularly intense. This radiation, which is called synchrotron radiation after the first particle-accelerating machines wherein the phenomenon was observed, has long been considered a major drawback of circular accelerators for electrons.
The seventies saw the development of specialized laboratories putting non-coherent, polychromatic, synchrotron radiation to use in studies on the structure of condensed matter. The synchroton light is pulsed whenever the electron beam passes before the radiation-extraction window. This pulsed light, with very brief and highly characterized pulses, is well suited to kinematic studies at time scales from the picosecond range to the millisecond range.
Just like the radiation emitted by a standard laser, a radiation that is coherent in phase and monochromatic can be obtained generally around relativistic beams by subjecting the electrons to periodic deviations perpendicular to their mean trajectory. This is the principle of the structure of the "free electron laser" working, again in the relativistic field, on the basis of the time-contraction effect, between a reference frame related to the beam and a fixed reference frame, the deviations "seen by the beam" being observable in the fixed reference frame at a far higher frequency.
The radiation of a free electron laser comes from the addition of the radiations emitted by each of the "sources" formed by the deviations of beams and is therefore not homogeneous in the space surrounding the sources, because the radiations coming from the different sources are not in step with one another at a given point. Because of the phase relationships among the sources created by the shape of the wiggler, the radiation of a free electron laser is coherent.
The device used to obtain the periodic deviations of the electrons is called a "wiggler" because, in its simplest design, the device makes the path of the electrons "wiggle". It is easy to imagine the waves described by the path of the electrons when they go through a region where alternating magnetic or electrical fields deflect the electrons in either of the directions perpendicular to that of their velocity.
The alternating fields of the wiggler can be obtained by the alternation of permanent magnets or by making current flow in coils around the path of the beam. The geometry of such devices around the beam determines the interaction with the electrons so as to "wiggle" their paths and obtain the laser effect.
It would appear, furthermore, that for industrial-scale applications, wigglers with permanent magnets have numerous advantages over double helix wigglers in which the fields are produced by making currents flow in helical coils. For, wigglers with permanent magnets make it possible to avoid the consumption and heat dissipation problems associated with wigglers supplied with current. Furthermore, in the case of short pulses, the need for synchronization between the supplies of the wiggler and the beam is removed. For continuous applications, the usefulness of permanent magnets is obvious.
In practical wiggler structures, the magnetic fields chiefly have two geometries: either a geometry of linear polarization, perpendicular to the path of the electrons, or a geometry of helical polarization.
Helical polarization has the advantage of preventing the problem of the drift of the beam in a magnetic guiding field and possesses a higher degree of symmetry. In particular, the longitudinal component of the magnetic field is zero on the axis. Furthermore, this polarization focuses the beam in two dimensions.
To obtain the optimum functioning of the free electron laser (FEL), the electron beam has to be injected into a wiggler with adiabatic insertion. This means that the fields of the wiggler rise towards their maximum value gradually from the point where the electrons are injected.
The adiabatic profile may be obtained in different ways: by magnetic diffusion when the wiggler field is obtained by a current pulse, by changing the radius of the helical coils, or by shunting the current the flows in the wiggler. In the prior art wigglers with permanent magnets, the adiabatic profile can be obtained by giving the wiggler field a stepped profile using metal pieces of variable thickness and high magnetic permeability. It must be noted that this rules out the use of this type of wiggler in conjunction with an external focusing field because the parts that create the stepped profile disturb both the wiggler field and the guiding field, the latter being indispensable to any application of power under high current.
The present invention enables these drawbacks to be overcome while at the same time making it possible to obtain a continuous and adiabatic increase of the magnetic field in the insertion region.